The middle term in the expansion of ${(1 + x)^{2n}}$ is
$\frac{{(2n)!}}{{n!}}{x^2}$
$\frac{{(2n)!}}{{n!(n - 1)!}}{x^{n + 1}}$
$\frac{{(2n)!}}{{{{(n!)}^2}}}{x^n}$
$\frac{{(2n)!}}{{(n + 1)!(n - 1)!}}\,{x^n}$
The number of rational terms in the binomial expansion of $\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)^{120}$ is $....$
The largest term in the expansion of ${(3 + 2x)^{50}}$ where $x = \frac{1}{5}$ is
The coefficient of $x^{18}$ in the product $(1+ x)(1- x)^{10} (1+ x + x^2 )^9$ is
The middle term in the expression of ${\left( {x - \frac{1}{x}} \right)^{18}}$ is
The coefficient of $x ^7$ in $\left(1-x+2 x^3\right)^{10}$ is $........$.